The invention relates to wavelet transform of an arbitrary shape object and more particularly to an arbitrary shape wavelet transform with phase alignment (ASWP).
Compared with coding a whole rectangular image, coding of individual objects in a nonrectangular shape has numerous advantages in coding efficiency and functionality. Such coding requires coding of the shape mask and the content image. The binary shape mask can be encoded by modified modified READ or context adaptive arithmetic coding. The arbitrary shape content image is transformed into the transform domain, quantized and entropy encoded. Since the content image is not of a rectangular shape, regular DCT and wavelet transforms can not be applied directly.
There are a number of approaches for transforming an arbitrary shape content image. The most popular approach is padding which is described by Z. Wu and T. Kanamaru, "Block-based DCT and wavelet selective coding for arbitrarily shaped images", Visual Communication and Image Processing'97, SPIE Vol. 3024, pp. 658-665, January 1997, San Jose, Calif. With padding, the image is segmented into fixed size blocks. Only those blocks that contain at least one object pixel are encoded. For blocks that are not fully occupied by the object, the remaining pixels are padded repeatedly with nearby object pixels. Since padding increases the number of coefficients to be coded, coding efficiency is significantly decreased. An improved version of the padding approach is described by J. Moon, G. Park, S. Chun and S. Choi, "Shape-adaptive region partitioning method for shape-assisted block-based texture coding", IEEE Trans. on Circuits and Systems for Video Technology, vol. 7, no.1, pp.240-246, February 1997. In Moon et al., block positions are systematically changed to reduce the number of blocks that need to be coded and the number of coefficients that need to be padded.
A wavelet padding approach is described by H. Katata, N. Ito, T. Anno and H. Kusao, "Object wavelet transform for coding of arbitrarily shaped image segments", IEEE Trans. on Circuits and Systems for Video Technology, vol. 7, no. 1, pp.235-237, February 1997. In Katata, et. al., padding is restricted to a small region around the original object. Although these techniques reduce the number of coefficients to be padded, padding is still required.
A shape-adaptive (SA) DCT is described by P. Kauff, B. Makai, S. Rauthenberg, U. Golz, J. Lameillieure and T. Sikora, "Functional coding of video using a shape-adaptive DCT algorithm and an object-based motion prediction toolbox", IEEE Trans. on Circuits and systems and Video Technology, vol. 7, no. 1, pp.181-196, February 1997. The shape-adaptive (SA) DCT avoids padding in block based DCTs. To apply the DCT to a block not fully occupied by the object, SA-DCT first moves all pixels toward the upper block boundary. A variable basis DCT is applied independently to each column with the DCT basis equal to the number of coefficients in each column. After SA-DCT in the vertical direction, the pixels are moved toward the left block boundary, and a similar variable basis DCT with basis corresponding to the number of coefficients in each row are applied horizontally.
Although SA-DCT avoids padding, there are several disadvantages in terms of transform efficiency and implementation complexity. The variable basis DCT used in SA-DCT has no fast algorithms. It is also not separable and the result is different if the horizontal transform is applied first. Transform efficiency is reduced because the neighboring pixels in the horizontal transform might not be the neighboring pixels in the original image. A nonpadding shape adaptive wavelet transform is described by W. Li and S. Li, "Shape-adaptive discrete wavelet transform for coding arbitrarily type shaped texture", Visual Communication and Image Processing'97, SPIE Vol. 3024, pp. 1046-1056, January 1997, San Jose, Calif. Whenever the data length is longer than the wavelet filter, if the data length is even, the data is directly transformed with a circular wavelet transform, if the data length is odd, the data is truncated to the next even length and transformed again with the circular wavelet transform, the extra pixel is copied directly to the low pass band. A Haar transform is adopted whenever the wavelet filter length is longer than the data. This technique is complex as there are several modes of the transform. The transform efficiency is also reduced since the Haar transform adopted when the data length is short is not very efficient, and in a 2D transform, the subsequent vertical transform is not applied on the phase aligned horizontal transform coefficients.
Thus a need remains to improve the transform efficiency for encoding arbitrary shaped objects.